Question

Number of minimum cubes of side 4 cm are needed to make another cube, whose lateral surface area is x cm 2 is
1)4,x=64
2)8, x = 256
3)4, x = 96
4)8, x = 384

Answer 1

Given : cubes of side 4 cm are needed to make another cube, whose lateral surface area is x cm²

To Find : Minimum number of cubes required and value of x

1)4,x=64

2)8, x = 256

3)4, x = 96

4)8, x = 384

Solution:

let say cube size is 4n cm x 4n cm  x 4n cm

then n³  Cubes are required  ( (4n)³/4³) = n³)

Lateral  Surface area  = 4(4n)² = 64n² cm²

lateral surface area is x cm²

64n² = x

n = 1  means that original cube itself

Hence  Smallest possible value of n = 2

=> 64(2)² = x

=> x = 256

cubes required =  n³  = 2³ = 8

cubes required  = 8

x = 256

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